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Consider, for example, a baseball, pitched as a gyroball, so that its spin axis is aligned with the direction of the pitch. It will have one helicity with respect to the point of view of the players on the field, but would appear to have a flipped helicity in any frame moving faster than the ball.
Helicity is a pseudo-scalar quantity: it changes sign under change from a right-handed to a left-handed frame of reference; it can be considered as a measure of the handedness (or chirality) of the flow. Helicity is one of the four known integral invariants of the Euler equations; the other three are energy, momentum and angular momentum.
To see an in depth discussion of the two with examples, which also shows how chirality and helicity approach the same thing as speed approaches that of light, click the link entitled "Chirality and Helicity in Depth" on the same page. History of science: parity violation; Helicity, Chirality, Mass, and the Higgs (Quantum Diaries blog)
In statistical mechanics, the Zimm–Bragg model is a helix-coil transition model that describes helix-coil transitions of macromolecules, usually polymer chains. Most models provide a reasonable approximation of the fractional helicity of a given polypeptide; the Zimm–Bragg model differs by incorporating the ease of propagation (self-replication) with respect to nucleation.
Helicity indicates the orientations of the spin and translational momentum vectors. [29] Helicity is frame-dependent because of the 3-momentum in the definition, and is quantized due to spin quantization, which has discrete positive values for parallel alignment, and negative values for antiparallel alignment.
One scheme of nomenclature in based on envisioning the helicity defined by these groups. [11] Starting with the substituent of highest priority in the closest ring and moving along the shortest path to the substituent of highest priority in the other ring, the absolute configuration is assigned P or Δ for clockwise and M or Λ for ...
An example of a molecule that does not have a mirror plane or an inversion and yet would be considered achiral is 1,1-difluoro-2,2-dichlorocyclohexane (or 1,1-difluoro-3,3-dichlorocyclohexane). This may exist in many conformers ( conformational isomers ), but none of them has a mirror plane.
For example, conservation of electric charge q is = where ∇⋅ is the divergence operator, ρ is the density of q (amount per unit volume), j is the flux of q (amount crossing a unit area in unit time), and t is time.